The present invention concerns optical systems such as an optical sampling digital oscilloscope, and pertains particularly to increased wavelength coverage in nonlinear optics by nonuniformly chirped quasi-phase matching.
Nonlinear crystals are used in optical frequency (OF) mixers within optical fiber communication systems and other optical signal processing systems. Typical second-order polarization coefficients in nonlinear crystals range from a few tenths to a few hundred picometers per volt (pm/V). This level of nonlinearity pales in comparison to that of electronic diodes. Efficient optical mixing using nonlinear crystals requires accumulation over interaction lengths that are orders of magnitude greater than the wavelength.
In an application where an optical signal is mixed with a strobe signal, for modest optical pump power and modest nonlinear coefficient, long nonlinear crystals can be used. However, net accumulation only occurs correctly if the total input photon momentum equals the total output photon momentum to the limit imposed by the uncertainty principle. The shorter the interaction length the greater the allowable momentum error. When viewing light as a wave (versus using a particle description), this is equivalent to requiring phase matching between the output electromagnetic wave and the product of the input waves.
In the past, phase matching has been accomplished in one of four ways. A first way is angle-tuning in birefringent single crystals. A second way is working with a higher-order waveguide mode for the shortest wavelength in the process. A third way, currently being researched, is using photonic crystal design phase matching to modify the linear properties in an appropriate wavelength-dependent fashion.
A fourth way to accomplish phase matching is to use quasi-phase-matching (QPM). When using QPM, crystal domains are periodically reversed to alternate the sign of the nonlinear product polarization while maintaining all of the linear properties. QPM has been implemented by periodic electric-field poling of ferroelectric crystals. Periodically poled lithium niobate (PPLN), for example, is commonly used for QPM. Periodic-poling is accomplished by periodically inverting the crystal structure on the scale of a few microns. QPM has also been implemented by periodic oriented/anti-oriented crystal growth on periodically surface-modified substrates in the zincblende class, although this technique has not enjoyed much success. For further information on QPM, see for example, Martin M. Fejer, et al., xe2x80x9cQuasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerancesxe2x80x9d, IEEE Journal of Quantum Electronics, Vol. 28, No. 11, November 1992.
Due to inevitable index of refraction dispersion, all known phase-matching methods have limited spectral acceptance. Indices become singular as the crystal""s bandgap is approached. In known phase-matching methods, mixing efficiency peaks at a given design wavelength, but this efficiency drops off as the input wavelength is detuned. The spectral acceptance is inversely proportional to the interaction length. That is, high efficiency and large wavelength coverage are difficult to obtain simultaneously. In most cases, the second way (working with a higher-order waveguide mode for the shortest wavelength in the process) and the third way (phase matching to modify the linear properties in an appropriate wavelength-dependent fashion via photonic crystal design) described above only exacerbate the situation since geometric-related dispersion tends to be much greater than the bulk material dispersion.
In typical prior art implementations of QPM, the poling period is constant across the nonlinear crystal. However, it has been suggested to insert pseudorandom domain reversals to xe2x80x9cdigitally ditherxe2x80x9d an otherwise periodic pattern. See, Moshe Nazarathy and D. W. Dolfi, xe2x80x9cSpread-spectrum nonlinear-optical interactions: quasi-phase matching with pseudorandom polarity reversalsxe2x80x9d, Optics Letters, Vol. 12, page 823, October 1987.
In accordance with the preferred embodiment of the present invention a nonlinear crystal is used for mixing focused optical signals. The nonlinear crystal includes a plurality of domains. The domains are arranged serially across the nonlinear crystal. The domains have alternating polarity. The poling periods of the domains are varied across the nonlinear crystal so as to provide nonuniform chirping of phase matching of focused optical signals propagated through the nonlinear crystal.